Binary classification may be the most encountered problems in real-world applications and has
been extensively studied.
The standard binary model seeks to learn a classifier by maximizing the Accuracy Rate (AR)
or minimizing the error rate. However, the accuracy rate is not an appropriate metric in the setting
where the label class is imbalanced [1]}, [2]}, [3]}, [4]}.
A simple majority algorithm can guarantee a high prediction accuracy in such a case.
Many algorithms were devised to deal with imbalanced classification problems,
based on the cost-sensitive learning and resampling techniques [5]}, [6]}, [7]}, [8]}, [9]}, [10]}.
A comprehensive survey on related works can be found in [7]}, [12]}, [13]}.
The classical imbalanced learning algorithms aim at maximizing a modified accuracy rate.
Several other evaluation metrics have been proposed to measure the learned classifier, including AUC,
\(F_\beta \) -measure, and the geometric mean of the True Positive Rate (TPR) and
the True Negative Rate (TNR) [14]}, [15]}, [16]},
which are more appropriate for imbalanced classification tasks.
But, different from the accuracy rate, these measures can not be expressed as a sum of independent
metrics on individual examples and thus are called non-decomposable performance measures.
They give a more holistic evaluation of the entire data, which makes them challenging to be optimized.
